CN113269057B - Motor rotor fault prediction method based on confidence rule base reasoning - Google Patents

Abstract

The invention discloses a motor rotor fault prediction method based on confidence rule base reasoning. According to the invention, vibration acceleration signals are firstly collected at different positions of a motor rotor, the vibration acceleration signals are converted into frequency domain signals through a fast Fourier transform method, the amplitude of 1 frequency multiplication is taken as a fault characteristic variable, the collected different fault characteristic variable values are respectively sequenced in a time sequence to obtain a reference evidence matrix corresponding to a reference value set and a fault type mapping relation, then a corresponding BRB model is established for each fault characteristic variable, and prediction evidence can be obtained according to a predicted value and a corresponding REM. And finally, constructing a fault information fusion decision model, fusing the obtained prediction evidence, wherein the input of the information fusion decision model is the predicted value of all fault characteristic variables, and the output is the fault type of the motor rotor at the future moment. The model of the invention has better precision, can timely and accurately predict the fault type, and is convenient for engineering realization.

Description

Motor rotor fault prediction method based on confidence rule base reasoning

Technical Field

The invention relates to a motor rotor fault prediction method based on confidence rule base (BRB) reasoning, and belongs to the technical field of industrial equipment state detection and fault diagnosis.

Background

The motor rotor is taken as a main component of motor equipment, and any unbalance faults appear in the motor rotor can have great influence on the operation of the motor and the normal operation of the equipment. The motor rotor unbalance fault prediction is a main means for guaranteeing the production safety and stability of the industrial field in which the motor participates, and can predict faults in advance so as to effectively avoid major accidents. Under normal conditions, the centrifugal force of the motor rotor reaches balance, the motor is in a static, dynamic and even balance state, power required in industrial production can be provided, speed regulation and the like of the motor can be realized, and the safety operation of motor equipment is greatly influenced.

However, the motor belongs to high-power electrical equipment, a large amount of heat energy and mechanical abrasion are generated during operation, if unbalance faults occur on a motor rotor, the motor is greatly influenced, the safety of equipment operated by the motor can be directly influenced, and once the safety of the equipment is problematic, certain property and other losses are brought. Therefore, in order to ensure the normal operation of the devices, the motor rotor needs to be in a balanced state, so that the motor rotor unbalance fault prediction method can be researched to predict the motor rotor unbalance fault in advance, further avoid larger loss caused by the problems of the motor, and provide a guarantee for the safe operation of the motor devices.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a motor rotor fault prediction method based on confidence rule base reasoning.

Firstly, collecting vibration acceleration signals at different positions of a motor rotor, converting the vibration acceleration signals into frequency domain signals through a fast Fourier transform method, taking amplitude of 1 times of frequency as a fault characteristic variable, respectively sequencing the collected different fault characteristic variable values according to a time sequence to obtain a Reference Evidence Matrix (REM) corresponding to a reference value set and a fault type mapping relation, then establishing a corresponding BRB model for each fault characteristic variable, wherein the input of the model is different sampling values corresponding to the fault characteristic variable, the output is a predicted value of the fault characteristic variable at the future time, the predicted value and the corresponding REM can obtain predicted evidence, finally, constructing a fault information fusion decision model, fusing the obtained predicted evidence, wherein the input of the fault information fusion decision model is the predicted value of all the fault characteristic variables, and the output is the fault type of the motor rotor at the future time. The method can be used for predicting the motor rotor fault type at the future moment by utilizing the motor rotor fault characteristic variable values collected by the vibration acceleration sensor which is low in cost and can be simply installed.

The invention comprises the following steps:

(1) Setting a motor rotor unbalance fault set Θ= { F ₁,F₂,...,F_h,...,F_H|h＝1,2,...,H},F_h to represent the H fault in the fault set Θ, wherein H >3 is the number of fault categories;

(2) Under different unbalanced fault categories of the motor rotor, collecting vibration acceleration signals at J >3 different positions of the motor rotor, converting the vibration acceleration signals into frequency domain signals by using a fast Fourier transform method, taking the amplitude of 1 frequency multiplication as a fault characteristic variable, and recording the fault characteristic variable as { f _j |j=1, 2., J }, and obtaining J fault characteristic variables;

(3) For J fault characteristic variables, respectively designing corresponding BRB models to predict the characteristic variables, and setting a sampling value of the fault characteristic variable f _j to be represented by f _j,t, wherein t epsilon N ⁺ is a sampling time, N ⁺ is an infinite positive integer, for the input of the BRB _j model corresponding to the jth fault characteristic variable f _j to be { f _j,t-l+1,...,f_j,t-1,f_j,t }, l >1 is the number of model inputs, and an output variable y _j,t+o represents a predicted value of the fault characteristic variable value f _j,t+o at a future time t+o, wherein o >0 is the o-th time after the current time t;

(3-1) in the BRB _j model, f _j,t-l+1,...,f_j,t-1,f_j,t is respectively marked as a variable x ₁,x₂,...,x_n...,x_l, and the set of model input reference values is

Wherein R >1 is the number of reference values for each input, x _n is the value of the fault characteristic variable for the nth input of the model,Wherein/>Is the reference value of the nth input's r reference level, and the reference value set of the output y _j,t+o is:

D^j＝{D_i ^j|j＝1,2,...,J；i＝1,2,…,N} (2)

Wherein D₁ ^j<D₂ ^j<…<D_i ^j<…<D_N ^j,D_i ^j is the reference value of the i-th reference level output, N >1 is the number of the output reference values, and a rule base BRBj is constructed based on the number of the output reference values;

(3-2) the rule base BRBj constructed by K rules, the value of K being the product of the number of all the inputted reference values in the BRB _j model, wherein the kth rule R _k is described as

Wherein,Representing the reference value corresponding to the nth input fault characteristic variable value x _n of the model in the kth rule, m _i,k is the confidence coefficient corresponding to D _i ^j under the kth rule, and meets the/>, under the kth rule

(3-3) After the sampling sequence f _j,t-l+1,...,f_j,t-1,f_j,t is obtained at the time t, the input x ₁＝f_j,t-l+1,x₂＝f_j,t-l+2,...,x_l＝f_j,t of the BRBj model can be obtained, and the matching degree of each input corresponding to the reference value is calculated, which comprises the following specific steps:

(a) When (when) Or/>When x _n pair/>And/>The values of the matching degree alpha _n,1 and alpha _n,R are 1, and the matching degree of other reference values is 0;

(b) When (when) When p=2, 3, …, R-1, x _n is for/>And/>The matching degree of (a) is respectively

At this time, the matching degree of the model input x _n to other reference values is 0;

(3-4) calculating BRBj the activation weight corresponding to the kth rule activated by each input x ₁,x₂,...,x_l of the model according to the matching degree of the input corresponding to the reference value obtained in the step (3-3) Is that

Wherein the method comprises the steps ofInputting x _n for the model under the kth rule corresponding to the reference value/>Matching degree of/>The weight of the kth rule is that lambda ⁿ is more than or equal to 0 and less than or equal to 1, and the reliability of the nth input of the model is the weight of the kth rule;

(3-5) obtaining the activation weight of the kth rule according to step (3-4) Then fusing the confidence coefficient m _i,k corresponding to D _i ^j under the kth rule, and obtaining the confidence coefficient supporting D _i ^j after fusing all rules

(3-6) Calculating the predicted value y _j,t+o of the future t+o time f _j,t+o as

(4) Obtaining a corresponding BRB _j model according to the step (3) for each fault characteristic variable f _j, and obtaining predicted values y _j,t+o of J fault characteristic variables on line;

(5) The method comprises the following specific steps of:

(5-1) setting the reference value set of the fault signature variable f _j still using the reference value set D _i ^j in the formula (2), denoted a _j＝{A_j,i |j=1, 2,..j; i=1, 2, …, N }, wherein A_j,1＝D_i ^j,A_1,2＝D₂ ^j,...,A_j,i＝D_i ^j,A_j,N＝D_N ^j,A_j,i is the ith reference level corresponding to the jth fault signature variable f _j, and a set of "sample pairs" is obtained from the fault signature variable samples collected in steps (1) - (3) and the fault types corresponding to the fault signature variable samples, and is denoted as U = { (f _j,t,F_h) };

(5-2) establishing a reference evidence matrix (REM _j) of the mapping relation between the reference value set A _j corresponding to the fault characteristic variable F _j and the fault type F _h according to the sample pair set U, see Table 1

Table 1 f _j reference evidence matrix

Wherein,Is the confidence of the j-th fault signature variable F _j corresponding to the i-th reference level supporting fault type F _h and it supports the confidence sum/>, of all fault typesEach column confidence in REMj is noted as reference evidence/>, corresponding to reference value a _j,i Establishing a corresponding REMj for each fault characteristic variable f _j, and establishing J total fault characteristic variables;

(5-3) taking the predicted value y _j,t+o of the fault characteristic variable f _j in the step (4) as the input of a fault information fusion decision model, activating evidence e _j, wherein the specific process is as follows:

(a) When y _j,t+o≤A_j,1 or y _j,t+o≥A_j,N, y _j,t+o takes on 1 for the similarities eta _j,1 and eta _j,N of A _j,1 and A _j,N, and takes on 0 for the similarities of other reference values;

(b) When a _j,q≤y_j,t+o≤A_j,q+1, q=2, 3, …, N-1, x _n match a _j,q and a _j,q+1, respectively

η_j,q＝(A_j,q+1-y_j,t+o)/(A_j,q+1-A_j,q) (8a)

η_j,q+1＝(y_j,t+o-A_j,q)/(A_j,q+1-A_j,q) (8b)

At this time, the matching degree of y _j,t+o to other reference values is 0;

(c) For the input predicted value y _j,t+o, it will fall into the interval formed by two reference values [ A _j,i,A_j,i+1 ], where the two reference values correspond to evidence And/>Activated, then the evidence of y _j,t+o may be evidence/>, by the reference valueAnd/>Obtained in the form of a weighted sum

e_j＝{(F_h,p_h,j),h＝1,...,H} (9a)

(5-4) Obtaining J pieces of evidence altogether according to the step (5-3), taking the fault set Θ in the step (1) as a recognition frame, its power set being noted as P (Θ), being a set of all subsets of the set Θ, whereinSetting the evidence importance factor omega _j and the evidence reliability factor r _j to be equal, wherein r _j≤1,0≤ω_j is more than or equal to 0 and less than or equal to 1, and/(respectively)Then a piece of evidence in the Evidence Reasoning (ER) rule is expressed as

Wherein, the confidence levelRepresenting e _j pair propositions/>, taking into account both r _j and ω _j Is defined as the degree of support of

Wherein m _θ,j＝ω_jp_θ,j,c_rω,j＝1/(1+ω_j-r_j) is a normalization factor;

(5-5) fusing J pieces of evidence by utilizing ER rule to obtain a fusion result as

Z(f(t+o))＝{(F_h,p_h,e(J))|h＝1,2,...,H} (12)

J=1, 2, J, P _h,e(J) represents the joint support reliability of supporting the fault type F _h after merging all J pieces of evidence, F (t+o) = (F _1,t+o,f_2,t+o...,f_j,t+o...,f_J,t+o) is a predicted value vector of J BRB models corresponding to the moment t+o of the J fault feature variables, and Z (F (t+o)) makes a final decision to identify the fault class supported by the maximum reliability as the fault class to which the sample vector F (t+o) belongs.

The invention has the beneficial effects that: according to the invention, different fault characteristic variables can be acquired according to different fault characteristic variable values acquired by vibration acceleration sensors arranged at different positions of a motor rotor, corresponding BRB models are established, different fault characteristic variable values at future time are respectively predicted, further the fault type at future time can be predicted according to the predicted future time fault characteristic variable values and the established fault prediction information fusion decision model, and a good prediction effect can be achieved.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a sequence of 5 fault signature variable sample values collected under 5 fault types at different times in an embodiment of the method of the present invention;

FIG. 3 is a graph showing the predicted values and the actual values of 5 fault-characteristic variables at different moments in an embodiment of the method of the present invention.

Detailed description of the preferred embodiments

The invention provides a motor rotor fault prediction method based on confidence rule base reasoning, which is shown in a flow chart in figure 1 and comprises the following steps:

(1) Setting a motor rotor unbalance fault set Θ= { F ₁,F₂,...,F_h,...,F_H|h＝1,2,...,H},F_h to represent the H fault in the fault set Θ, wherein H >3 is the number of fault categories;

(2) Under different unbalanced fault categories of the motor rotor, collecting vibration acceleration signals at J >3 different positions of the motor rotor, converting the vibration acceleration signals into frequency domain signals by using a fast Fourier transform method, taking the amplitude of 1 frequency multiplication as a fault characteristic variable, and recording the fault characteristic variable as { f _j |j=1, 2., J }, and obtaining J fault characteristic variables;

(3) For J fault characteristic variables, respectively designing corresponding BRB models to predict the characteristic variables, and setting a sampling value of the fault characteristic variable f _j to be represented by f _j,t, wherein t epsilon N ⁺ is a sampling time, N ⁺ is an infinite positive integer, for the input of the BRB _j model corresponding to the jth fault characteristic variable f _j to be { f _j,t-l+1,...,f_j,t-1,f_j,t }, l >1 is the number of model inputs, and an output variable y _j,t+o represents a predicted value of the fault characteristic variable value f _j,t+o at a future time t+o, wherein o >0 is the o-th time after the current time t;

(3-1) in the BRB _j model, f _j,t-l+1,...,f_j,t-1,f_j,t is denoted as variable x ₁,x₂,...,x_n...,x_l, respectively, and the set of model input reference values is:

wherein R >1 is the number of reference values for each input, x _n is the value of the fault characteristic variable for the nth input of the model, Wherein/>Is the reference value of the nth input's r reference level, and the reference value set of the output y _j,t+o is:

D^j＝{D_i ^j|j＝1,2,...,J；i＝1,2,…,N} (2)

Wherein D₁ ^j<D₂ ^j<…<D_i ^j<…<D_N ^j,D_i ^j is the reference value of the i-th reference level output, N >1 is the number of the output reference values, and a rule base BRBj is constructed based on the number of the output reference values;

(3-2) the rule base BRBj constructed by K rules, the value of K being the product of the number of all the inputted reference values in the BRB _j model, wherein the kth rule R _k is described as

Wherein,Representing the reference value corresponding to the nth input fault characteristic variable value x _n of the model in the kth rule, m _i,k is the confidence coefficient corresponding to D _i ^j under the kth rule, and meets the/>, under the kth rule

(3-3) After the sampling sequence f _j,t-l+1,...,f_j,t-1,f_j,t is obtained at the time t, the input x ₁＝f_j,t-l+1,x₂＝f_j,t-l+2,...,x_l＝f_j,t of the BRBj model can be obtained, and the matching degree of each input corresponding to the reference value is calculated, which comprises the following specific steps:

(a) When (when) Or/>When x _n pair/>And/>The values of the matching degree alpha _n,1 and alpha _n,R are 1, and the matching degree of other reference values is 0;

(b) When (when) When p=2, 3, …, R-1, x _n is for/>And/>The matching degree of (a) is respectively

At this time, the matching degree of the model input x _n to other reference values is 0;

(3-4) calculating BRBj the activation weight corresponding to the kth rule activated by each input x ₁,x₂,...,x_l of the model according to the matching degree of the input corresponding to the reference value obtained in the step (3-3) Is that

Wherein the method comprises the steps ofInputting x _n for the model under the kth rule corresponding to the reference value/>Matching degree of/>The weight of the kth rule is that lambda ⁿ is more than or equal to 0 and less than or equal to 1, and the reliability of the nth input of the model is the weight of the kth rule;

(3-5) obtaining the activation weight of the kth rule according to step (3-4) Then fusing the confidence coefficient m _i,k corresponding to D _i ^j under the kth rule, and obtaining the confidence coefficient supporting D _i ^j after fusing all rules

(3-6) Calculating the predicted value y _j,t+o of the future t+o time f _j,t+o as

For ease of understanding, step (3) is illustrated herein by taking the fault characteristic variable f ₁ as an example, taking the fault characteristic variable values f _1,t-1 and f _1,t as the inputs x ₁ and x ₂ of the BRB ₁ model corresponding to the fault characteristic variable f ₁, where the reference value sets corresponding to the two inputs are the model a ¹＝{0,0.2000,0.4000},A²＝{0,0.2000,0.4000},BRB₁ output as f _1,t+1, the reference value set is D ¹ = {0,0.2000,0.4000}, and 9 rules are built in total, and the rule base is shown in table 2. To easily explain the problem, the weight of each rule is given byBoth are set to 1, and the reliability of both inputs λ ¹ and λ ² are also set to 1.

TABLE 2 rule base for fault signature variable f ₁

Sequencing the collected fault characteristic variable values according to a time sequence, assuming that the current time is t and the time t+o is t+1, obtaining x ₁＝f_1,t-1＝0.0826,x₂＝f_1,t =0.0465, and calculating the matching degree of the input x ₁ and x ₂ in the BRB ₁ model corresponding to the reference values according to the step (3-3) to obtain alpha _1,1＝0.413,α_1,2＝0.587,α_1,3＝0,α_2,1＝0.2325,α_2,2＝0.7675,α_2,3 =0, so that four rules in a rule base are activated, namely the 1 st rule, the 2 nd rule, the 4 th rule and the 5 th rule. Based on the set rule weights and the input reliability, the rule weights to be activated can be calculated by the formula (5) asAfter the confidence level of all the rules of fusion activation can be calculated according to the formula (6), the result is that m ₁＝0.705,m₂＝0.245,m₃ =0.05, and the predicted value y _1,t+1 =0.069 of the time f _1,t+1 of t+1 is obtained according to the formula (7).

(4) For each fault characteristic variable f _j, a corresponding BRB _j model can be obtained according to the step (3), and predicted values y _j,t+o of J fault characteristic variables are obtained online;

In order to facilitate understanding that a corresponding BRBj model is built for each fault-feature variable f _j, for example, there are a total of 5 motor rotor fault-feature variables, denoted as f ₁,f₂,f₃,f₄,f₅, respectively, and according to the method in step (3), another four BRB models, denoted as BRB ₁,BRB₂,BRB₃,BRB₄,BRB₅, are continuously built, and the time t+o of all models is set to be the time t+1, then all predicted values of the fault-feature variables at the time t+1 can be obtained together, denoted as y _1,t+1,y_2,t+1,y_3,t+1,y_4,t+1,y_5,t+1, respectively, and these values are denoted as predicted sample vectors, which are used as inputs for the next fault-information fusion decision model.

(5) The method comprises the following specific steps of:

(5-1) setting the reference value set of the fault signature variable f _j still using the reference value set D _i ^j in the formula (2), denoted a _j＝{A_j,i |j=1, 2,..j; i=1, 2, …, N }, wherein A_j,1＝D_i ^j,A_1,2＝D₂ ^j,...,A_j,i＝D_i ^j,A_j,N＝D_N ^j,A_j,i is the ith reference level corresponding to the jth fault signature variable f _j, and a set of "sample pairs" is obtained from the fault signature variable samples collected in steps (1) - (3) and the fault types corresponding to the fault signature variable samples, and is denoted as U = { (f _j,t,F_h) };

To facilitate an understanding of the "sample pair" set, examples are briefly described herein. Given that in the case of fault type F ₁, the fault characteristic sample values collected by the 5 sensors are F _1,t＝0.0465,f_2,t＝0.0309,f_3,t＝0.0137,f_4,t＝0.0150,f_5,t =0.0445, respectively, these sample values and the corresponding fault type F ₁ can be recorded as a sample pair, (0.0465, 0.0309,0.0137, 0.0130, 0.0445, F ₁). Similarly, in the case of fault type F ₂ samples of the fault signature variable at time t are taken, then the pair of samples for fault type F ₂ at this time is denoted (0.1935, 0.1636,0.0092,0.0153,0.0253, F ₂). At different times, sample pairs are also obtained for such fault signature variable values corresponding to the fault type, respectively.

(5-2) Establishing a reference evidence matrix (REM _j) of the mapping relation between the reference value set A _j corresponding to the fault characteristic variable F _j and the fault type F _h according to the sample pair set U, see Table 1

Table 1 f _j reference evidence matrix

Wherein,Is the confidence of the j-th fault signature variable F _j corresponding to the i-th reference level supporting fault type F _h and it supports the confidence sum/>, of all fault typesEach column confidence in REMj is noted as reference evidence/>, corresponding to reference value a _j,i Establishing a corresponding REMj for each fault characteristic variable f _j, and establishing J total fault characteristic variables;

For ease of understanding, REMj is illustrated herein to give a reference evidence matrix for two fault signature variables f ₁ and f ₂, as in tables 3 and 4 below.

Table 3 f ₁ reference evidence matrix

Table 4 f ₂ reference evidence matrix

Wherein, for f ₁, reference evidence matrix Table 3, evidenceWhen the fault characteristic variable F ₁ corresponds to the reference value 0, the confidence coefficient supporting the fault type F ₁ is 1, and the confidence coefficient supporting the other four fault types is 0. Evidence/>When the fault characteristic variable F ₂ corresponds to the reference value of 0.2000, the confidence coefficient of the support fault type F ₁ is 0.7843, the confidence coefficient of the support fault type F ₂ is 0.2035, the confidence coefficient of the support fault type F ₃ is 0.0098, the confidence coefficient of the support fault type F ₄ is 0.0024, and the confidence coefficient of the support fault type F ₅ is 0. Evidence/>The types of faults F ₁,F₂,F₃,F₄,F₅ supported are 0.0126,0.4006,0.3525,0.2334,0.0009 respectively.

Similarly, for reference evidence matrix table 4 for f ₂, evidenceAnd/>The confidence level supporting each fault type can be clearly obtained.

(5-3) Taking the predicted value y _j,t+o of the fault characteristic variable f _j in the step (4) as the input of a fault information fusion decision model, activating evidence e _j, wherein the specific process is as follows:

(a) When y _j,t+o≤A_j,1 or y _j,t+o≥A_j,N, y _j,t+o takes on 1 for the similarities eta _j,1 and eta _j,N of A _j,1 and A _j,N, and takes on 0 for the similarities of other reference values;

(b) When a _j,q≤y_j,t+o≤A_j,q+1, q=2, 3, …, N-1, x _n match a _j,q and a _j,q+1, respectively

η_j,q＝(A_j,q+1-y_j,t+o)/(A_j,q+1-A_j,q) (8a)

η_j,q+1＝(y_j,t+o-A_j,q)/(A_j,q+1-A_j,q) (8b)

At this time, the matching degree of y _j,t+o to other reference values is 0;

(c) For the input predicted value y _j,t+o, it will fall into the interval formed by two reference values [ A _j,i,A_j,i+1 ], where the two reference values correspond to evidence And/>Activated, then the evidence of y _j,t+o may be evidence/>, by the reference valueAnd/>Obtained in the form of a weighted sum

e_j＝{(F_h,p_h,j),h＝1,...,H} (9a)

To facilitate an understanding of the activation evidence e _j, a brief description is given here by way of example. Still along with the reference evidence matrices of tables 3 and 4 for fault signature variables f ₁ and f ₂, two fault signature variables were chosen for simple calculation in order to be able to simply illustrate the process of activating evidence e _j. At a certain time t, the predicted values of the fault-characteristic variables f ₁ and f ₂ obtained in step (4) are y _1,t+1 =0.1000 and y _2,t+1 =0.1800, respectively, and as can be seen from table 3, y _1,t+1 =0.1000 activates evidenceAnd/>The corresponding reference values are 0 and 0.2000, respectively. As can be seen from table 4, y _2,t+1 =0.1800 activation evidence/>And/>The corresponding reference values are 0.1500 and 0.3500, respectively. From the formula (8 a) and the formula (8 b), it can be calculated that the predicted value y _1,t+1 =0.1000 matches η _1,1 =0.5 with respect to the reference value 0, and matches η _1,2 =0.5 with respect to the reference value 0.2000. Similarly, the predicted value y _2,t+1 =0.1800 matches η _2,2 =0.8500 with respect to the reference value 0.1500, and the predicted value y _2,3 =0.1500 matches with respect to the reference value 0.3500.

Further, the confidence coefficient p _1,1 =0.5x1.000+0.5x 0.7843 = 0.8921 of the support fault type F ₁, the confidence coefficient p _2,1 =0.5x0+0.5x 0.2035 = 0.1018 of the support fault type F ₂, the confidence coefficient p _3,1 =0.5x0+0.5x0.0098=0.0049 of the support fault type F ₃ are obtained according to the formulas (9 a) and (9 b), confidence p _4,1 =0.5x0+0.5x0.0024=0.0012 for support fault type F ₄, and confidence p _5,1 =0.5x0+0.5x0=0 for support fault type F ₅. Similarly, for y _2,t+1 =0.1800, a confidence level p _1,2 =0.85×0.2237+0.15×0= 0.1901 for support fault type F ₁, a confidence level p _2,2 =0.85×0.6779+0.15×0.1706= 0.6018 for support fault type F ₂, a confidence level p _3,2 =0.85×0.0547+0.15× 0.4441 = 0.1131 for support fault type F ₃, confidence p _4,2 =0.85×0.0437+0.15× 0.3775 =0.0938 for support failure type F ₄, confidence p _5,2 =0.85×0+0.15×0.0078=0.0012 for support failure type F ₅. Thus, evidence e₁＝{(F₁,0.8921)(F₂,0.1018)(F₃,0.0049)(F₄,0.0012)(F₅,0)}, predictive value y _2,t+1 =0.1800 for predictive value y _1,t+1 =0.1000 can be obtained e₂＝{(F₁,0.1901)(F₂,0.6018)(F₃,0.1131)(F₄,0.0938)(F₅,0.0012)}.

(5-4) Obtaining J pieces of evidence altogether according to the step (5-3), taking the fault set Θ in the step (1) as a recognition frame, its power set being noted as P (Θ), being a set of all subsets of the set Θ, whereinSetting the evidence importance factor omega _j and the evidence reliability factor r _j to be equal, wherein r _j≤1,0≤ω_j is more than or equal to 0 and less than or equal to 1, and/(respectively)Then a piece of evidence in the Evidence Reasoning (ER) rule is expressed as

Wherein, the confidence levelRepresenting e _j pair propositions/>, taking into account both r _i and ω _j Is defined as the degree of support of

Wherein m _θ,j＝ω_jp_θ,j,c_rω,j＝1/(1+ω_j-r_j) is a normalization factor;

(5-5) fusing J pieces of evidence by utilizing ER rule to obtain a fusion result as

Z(f(t+o))＝{(F_h,p_h,e(J))|h＝1,2,...,H} (12)

J=1, 2, J, P _h,e(J) represents the joint support reliability of supporting the fault type F _h after merging all J pieces of evidence, F (t+o) = (F _1,t+o,f_2,t+o...,f_j,t+o...,f_J,t+o) is a predicted value vector of J BRB models corresponding to the moment t+o of the J fault feature variables, and Z (F (t+o)) makes a final decision to identify the fault class supported by the maximum reliability as the fault class to which the sample vector F (t+o) belongs.

To facilitate an understanding of the fusion of all evidence, a brief description is given here by way of example. Still taking two fault characteristic variables as an example, the evidences e ₁ and e ₂ obtained in the step (5-3) are additionally set with an evidence importance factor ω _j =1, and the reliability factor r _j =1 of the evidence can be calculated according to formulas (10) - (13), and the result of merging the evidences e ₁ and e ₂ is that Z(f(t+1))＝Z(f_1,t+1,,f_2,t+1)＝{(F₁,0.7861)(F₂,0.1532)(F₂,0.0325)(F₂,0.0175)(F₂,0.0107)}, has the maximum probability of occurrence corresponding to the fault type F ₁ and is 0.7861, so that the fault type F ₁ at the time t+1 can be predicted to occur.

Embodiments of the method of the present invention are described in detail below with reference to the attached drawing figures:

The main flow chart of the method is shown in fig. 1, and the main contents are as follows:

According to different fault characteristic variable values acquired by vibration acceleration sensors arranged at different positions of a motor rotor, a corresponding BRB model can be established, and different fault characteristic variable values at future time can be respectively predicted. Similarly, a reference evidence matrix of the corresponding fault characteristic variable can be obtained by the sampling value of each fault characteristic variable, and predicted evidence can be obtained by combining the future time fault characteristic variable value predicted by each BRB model with the corresponding reference evidence matrix of the fault characteristic variable. And then all prediction evidences can be fused according to the fault prediction information fusion decision model, and the fault type at the future moment is predicted.

The following is combined with a certain ZHS-2 multifunctional motor flexible rotor experimental platform to introduce relevant detailed steps, and the performance of the motor rotor fault prediction method based on confidence rule base reasoning is verified through experimental results.

1. And simulating 5 unbalanced fault types of the motor rotor, acquiring fault characteristic variable values f ₁,f₂,f₃,f₄ and f ₅ of 5 vibration acceleration sensors installed at different positions on the experimental platform on line, sampling once every 3s, and acquiring 200 times of each fault type. Each fault type is commonly determined by 5 fault characteristic variable values, and fig. 2 is a sequence of fault characteristic variable value sampling collected under 5 fault types at different moments.

2. Establishing 9 rules in total, and establishing the weight of each rule, wherein reference value sets corresponding to two inputs of a BRB model BRB ₁,BRB₁ model of a fault characteristic variable f ₁ are respectively an A ¹＝{0,0.2,0.4},A²＝{0,0.2,0.4},BRB₁ model output reference value set of D ¹ = {0,0.2,0.4}, and the weight of each rule is equal to the weight of each ruleLet 1, the reliability of both inputs of the brb ₁ model, λ ¹ and λ ², are also set to 1. The rule base for the fault signature variable f ₁ is as follows in table 2.

TABLE 2 rule base for fault signature variable f ₁

And (3) repeating the steps (1) to (3), building BRB models corresponding to the other 4 fault characteristic variables, building 5 BRB models in total, and setting the current time as t and the future time t+o as t+1, so that predicted values of the future time t+1 corresponding to the 5 fault characteristic variables can be obtained. Dividing the sample value of the fault characteristic variable acquired in the step (2) and the corresponding fault type into sample pair sets as shown in the step (5-1), obtaining 5 reference evidence matrixes of a reference value set corresponding to the fault characteristic variables f ₁,f₂,f₃,f₄ and f ₅ and a fault type mapping relation, combining predicted values of the fault characteristic variable at the time t+1 given by 5 BRB models, obtaining predicted evidence corresponding to each predicted value of the fault characteristic variable according to the step (5-3), and obtaining 5 pieces of predicted evidence in total, namely e ₁、e₂、e₃、e₄ and e ₅ respectively. And then fusing the 5 pieces of obtained prediction evidence according to the step (5-4) and the step (5-5), and deciding the fault type at the future time t+1.

Test data obtained at all sampling times were subjected to experiments according to the above calculation procedure, and the confusion matrix of the failure prediction results is shown in table 5, from which it was found that the average diagnosis rate for 5 failure modes was 96.2%. Fig. 3 is a comparison chart of predicted values and actual values of 5 fault characteristic variables at different moments in one experiment, and it can be seen that the BRB model established according to steps (1) to (3) can accurately predict future values of the fault characteristic variables, and the effectiveness of the method is verified by combining the average diagnosis rates of 5 fault modes.

TABLE 5 confusion matrix for predicted outcomes

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Claims (1)

1. A motor rotor fault prediction method based on confidence rule base reasoning is characterized by comprising the following steps:

(1) Setting a motor rotor unbalance fault set Q= { F ₁,F₂,...,F_h,...,F_H|h＝1,2,...,H},F_h to represent the H fault in the fault set Q, wherein H >3 is the number of fault categories;

(2) Under different unbalanced fault categories of the motor rotor, collecting vibration acceleration signals at J >3 different positions of the motor rotor, converting the vibration acceleration signals into frequency domain signals by using a fast Fourier transform method, taking the amplitude of 1 frequency multiplication as a fault characteristic variable, and recording the fault characteristic variable as { f _j |j=1, 2., J }, and obtaining J fault characteristic variables;

(3) For J fault characteristic variables, respectively designing corresponding BRB models to predict the characteristic variables, and setting a sampling value of the fault characteristic variable f _j to be represented by f _j,t, wherein t epsilon N ⁺ is a sampling time, N ⁺ is an infinite positive integer, for the input of the BRB _j model corresponding to the jth fault characteristic variable f _j to be { f _j,t-l+1,...,f_j,t-1,f_j,t }, l >1 is the number of model inputs, and an output variable y _j,t+o represents a predicted value of the fault characteristic variable value f _j,t+o at a future time t+o, wherein o >0 is the o-th time after the current time t;

(3-1) in the BRB _j model, f _j,t-l+1,...,f_j,t-1,f_j,t is respectively marked as a variable x ₁,x₂,...,x_n...,x_l, and the set of model input reference values is

Wherein R >1 is the number of reference values for each input, x _n is the value of the fault characteristic variable for the nth input of the model,Wherein/>Is the reference value of the nth reference level of the nth input, and the reference value set of the output y _j,t+o is

D^j＝{D_i ^j|j＝1,2,...,J；i＝1,2,L,N} (2)

Wherein D₁ ^j<D₂ ^j<L<D_i ^j<L<D_N ^j,D_i ^j is the reference value of the i-th reference level output, N >1 is the number of the output reference values, and a rule base BRBj is constructed based on the number of the output reference values;

(3-2) the rule base BRBj constructed by K rules, the value of K being the product of the number of all the inputted reference values in the BRB _j model, wherein the kth rule R _k is described as

Wherein, Represents the reference value corresponding to the nth input fault characteristic variable value x _n of the model under the kth rule, m _i,k is the confidence coefficient corresponding to D _i ^j under the kth rule, and meets the/>, under the kth rule

(3-3) After the sampling sequence f _j,t-l+1,...,f_j,t-1,f_j,t is obtained at the time t, the input x ₁＝f_j,t-l+1,x₂＝f_j,t-l+2,...,x_l＝f_j,t of the BRBj model can be obtained, and the matching degree of each input corresponding to the reference value is calculated, which comprises the following specific steps:

(a) When (when) Or/>When x _n pair/>And/>The values of the matching degree alpha _n,1 and alpha _n,R are 1, and the matching degree of other reference values is 0;

(b) When (when) When p=2, 3, …, R-1, x _n is for/>And/>The matching degree of (a) is respectively

At this time, the matching degree of the model input x _n to other reference values is 0;

(3-4) calculating BRBj the activation weight corresponding to the kth rule activated by each input x ₁,x₂,...,x_l of the model according to the matching degree of the input corresponding to the reference value obtained in the step (3-3) Is that

Wherein the method comprises the steps ofInputting x _n for the model under the kth rule corresponding to the reference value/>Matching degree of/>The weight of the kth rule is 0- ⁿ -1, and the reliability of the nth input of the model is the weight of the kth rule;

(3-5) obtaining the activation weight of the kth rule according to step (3-4) Then fusing the confidence coefficient m _i,k corresponding to D _i ^j under the kth rule, and obtaining the confidence coefficient supporting D _i ^j after fusing all rules

(3-6) Calculating the predicted value y _j,t+o of the future t+o time f _j,t+o as

(4) Obtaining a corresponding BRB _j model according to the step (3) for each fault characteristic variable f _j, and obtaining predicted values y _j,t+o of J fault characteristic variables on line;

(5) The method comprises the following specific steps of:

(5-1) setting the reference value set of the fault signature variable f _j still using the reference value set D _i ^j in the formula (2), denoted a _j＝{A_j,i |j=1, 2,..j; i=1, 2, l, n }, wherein A_j,1＝D_i ^j,A_1,2＝D₂ ^j,...,A_j,i＝D_i ^j,A_j,N＝D_N ^j,A_j,i is the ith reference level corresponding to the jth fault signature variable f _j, and a set of "sample pairs" is obtained from the fault signature variable samples collected in steps (1) - (3) and the fault types corresponding thereto, denoted as U = { (f _j,t,F_h) };

(5-2) establishing a reference evidence matrix REM _j of the mapping relation between the reference value set A _j corresponding to the fault characteristic variable F _j and the fault type F _h according to the sample pair set U, see Table 1

Table 1f _j reference evidence matrix

Wherein,Is the confidence of the j-th fault signature variable F _j corresponding to the i-th reference level supporting fault type F _h and it supports the confidence sum/>, of all fault typesEach column confidence in REMj is noted as reference evidence/>, corresponding to reference value a _j,i Establishing a corresponding REMj for each fault characteristic variable f _j, and establishing J total fault characteristic variables;

(5-3) taking the predicted value y _j,t+o of the fault characteristic variable f _j in the step (4) as the input of a fault information fusion decision model, activating evidence e _j, wherein the specific process is as follows:

(a) When y _j,t+o￡A_j,1 or y _j,t+o 3A_j,N, the similarity h _j,1 and h _j,N of y _j,t+o to A _j,1 and A _j,N are both 1, and the similarity to other reference values is 0;

(b) When a _j,q￡y_j,t+o￡A_j,q+1, q=2, 3, …, N-1, x _n match a _j,q and a _j,q+1, respectively

h_j,q＝(A_j,q+1-y_j,t+o)/(A_j,q+1-A_j,q)(8a)

h_j,q+1＝(y_j,t+o-A_j,q)/(A_j,q+1-A_j,q)(8b)

At this time, the matching degree of y _j,t+o to other reference values is 0;

(c) For the input predicted value y _j,t+o, it will fall into the interval formed by two reference values [ A _j,i,A_j,i+1 ], where the two reference values correspond to evidence And/>Activated, then the evidence of y _j,t+o may be evidence/>, by the reference valueAnd/>Obtained in the form of a weighted sum

e_j＝{(F_h,p_h,j),h＝1,...,H}(9a)

(5-4) Obtaining J pieces of evidence in total according to the step (5-3), taking the fault set Q in the step (1) as an identification frame, the power set of which is noted as P (Θ), and the power set is a set of all subsets of the set Q, whereinSetting the evidence importance factor w _j and the evidence reliability factor r _j to be equal, wherein r _j≤1,0≤w_j is more than or equal to 0 and less than or equal to 1,/>A piece of evidence in the evidence reasoning ER rule is expressed as

Wherein, the confidence levelRepresenting e _j pair propositions/>, taking into account both r _j and w _j Is defined as the degree of support of

Wherein m _q,j＝w_jp_q,j,c_rw,j＝1/(1+w_j-r_j) is a normalization factor;

(5-5) fusing J pieces of evidence by utilizing ER rule to obtain a fusion result as

Z(f(t+o))＝{(F_h,p_h,e(J))|h＝1,2,...,H} (12)

J=1, 2, J, P _h,e(J) represents the joint support reliability of supporting the fault type F _h after merging all J pieces of evidence, F (t+o) = (F _1,t+o,f_2,t+o...,f_j,t+o...,f_J,t+o) is a predicted value vector of J BRB models corresponding to the moment t+o of the J fault feature variables, and Z (F (t+o)) makes a final decision to identify the fault class supported by the maximum reliability as the fault class to which the sample vector F (t+o) belongs.